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I have a GPS through-hole patch antenna, the through hole need to be connected to the bottom layer and then from there the feed-line flows to the GPS receiver. But I want the GPS receiver to be on top to be facing the sky so that means adding vias on the feed line which will change impedance, right?

I also have a question about the antenna ground plane since I'm a beginner in that field. My PCB is 4 layer with gnd plane as 2nd layer, can I use that as ground plane for the antenna or does the gnd plane of antenna has to be on the top layer directly underneath the antenna?

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A via has inductance , capacitance with inner layer pads and resistance but with Saturn's PCB Design tool, you can make it a 50 Ohm via, if that is what is needed.

Start with the effective dielectric constant for your f and material.

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If you add a transmission line to bottom also, don't forget you need to add also ground at the 3rd layer or use the 2nd layer ground but calculate the new impedance. It is also recommended to add ground via's surrounding the RF via. This helps bound all grounds of the multi-layer boards together in the most critical point (the RF transition). Look at it as a coaxial cable, a single wire surrounded by ground. Most Antennas require a free area of ground and all other lines and components above and below it, look carefully on the manufacturer recommendations and work accordingly.

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Via impedance question: If you must use a via, then pay attention to your return currents. For every wave there's a current path to the antenna and another path that goes away from the antenna. This path should be defined in capacitance and inductance in a way that it results in 50 ohms. If top and bottom signal layers do not share a common ground plane, think about placing a second via from one GND plane to the other in close proximity to the signal via. That way you don't create an unnecessary inductive loop. If you don't simulate it this won't be perfect but there shouldn't be a problem if you don't have perfect 50 ohms. This is usually not the case because of soldering pads and stuff like that. The effect is just a non-perfect match to the antenna which results in minimal reflections, hence not 100% of your transmitters power will be sent by the antenna - That phenomena is just normal if kept in boundaries. I personally use vias up to 3 GHz designs without problems but I take care of the current return path. (Think about that: Vias do not have inductance, but the loop that is created by the via and the return path. I recommend this for you to read: https://www.keysight.com/upload/cmc_upload/All/2_Demystifying_Vias_in_High-Speed_PCB_Designs.pdf)

GND-Plane question: This is a question which can only be answered by the datasheet of the manufacturer or antenna developer. If you choose to take the second layer as a GND plane, than you add dielectrium between the antenna and GND. Just stick with the recommendations of the manufacturer on how to place your ground.

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